• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,347 answers , 22,726 comments
1,470 users with positive rep
818 active unimported users
More ...

  What is a good introduction to integrable models in physics?

+ 9 like - 0 dislike

I would be interested in a good mathematician-friendly introduction to (exactly solvable)  integrable models in physics, either a book or expository article.

Related MathOverflow question: what-is-an-integrable-system.

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user Phira

asked Sep 22, 2011 in Resources and References by Phira (0 points) [ revision history ]
edited May 4, 2014 by dimension10
Do you have anything specific in mind? I think the term integrability is sometimes used in slightly different contexts.

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user Pieter Naaijkens
The fact that "integrability" can mean so many things sometimes makes the quest to learn about it so challenging! I have found the introductory sections of Etingoff's paper www-math.mit.edu/~etingof/zlecnew.pdf to be a very good mathematical reference for a particular, physically interesting system (Calogero-Moser) which describes particles interacting in one-dimension.

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user Eric Zaslow

6 Answers

+ 9 like - 0 dislike

I take "integrable models" to mean "exactly solvable models in statistical physics".

You can take a look at the classic book

Otherwise this new book is quit readable and covers more than just solvable models

Others can probably give you more mathematician-friendly references, but I think it would be good if you could be more specific about what you are looking for.

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user Heidar
answered Sep 22, 2011 by Heidar (855 points) [ no revision ]
Yes, "exactly solvable" is what I mean. Thanks, I will update my question later.

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user Phira
+ 6 like - 0 dislike
answered May 6, 2012 by Vijay Murthy (90 points) [ no revision ]
+ 2 like - 0 dislike

Another good recent book:

This post imported from StackExchange Physics at 2014-04-25 13:36 (UCT), posted by SE-user just-learning
answered Nov 16, 2013 by just-learning (95 points) [ no revision ]

Also see his lecture notes on integrability.

+ 2 like - 0 dislike

These lecture notes by Babelon could be quite helpful.

answered Aug 31, 2018 by a-user (40 points) [ no revision ]

There is a much more detailed ''Introduction to classical integrable systems'' by O. Babelon, D. Bernard, and M. Talon, very much recommended!

+ 1 like - 0 dislike

The slides from the lectures on integrable systems by Alexei Bolsinov from this course could be quite helpful (to get to the slides click on the Files tab at the above link). Also see the lecture notes by Boris Dubrovin "Integrable Systems and Riemann Surfaces".

answered Sep 5, 2018 by mathnphys (0 points) [ no revision ]
+ 1 like - 0 dislike

Specifically for integrable partial differential systems which are dispersionless a.k.a. hydrodynamic-type, i.e. can be written as quasilinear first-order homogeneous systems, in the case of two independent variables see these lecture notes, Section 3 of this article, and references therein; in the case of threeindependent variables see Section 3 of this same article,  subsubsection 10.3.3 of the Dunajski book mentioned by @just-learning, and these lecture notes, and references therein; for the case of four independent variables see introductory part of this article, the Dunajski book again, and references therein. 

answered Sep 7, 2018 by a-user (40 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights